Renate Kuenast, leader of the opposition Green party, said: "If you're serious about commemoration at such a place of horrors, then you don't pay such a visit during an election campaign."
Chief Rabbi Pinchas Goldschmidt, President of the Conference of European Rabbis, expressed his support for Mrs Merkel.
He said: "Mrs Merkel has absolutely nothing to prove regarding her commitment Holocaust memorial and suggestions that her visit to Dachau is disingenuous are quite offensive. Mrs Merkel was awarded the Lord Jakobovits Prize for European Jewry this year for the dedication she has shown throughout her life to learning the lessons of the Shoah."
No other German head of government has visited Dachau concentration camp.
